A shift of the two-photon resonance position is possible due to differing mean-field shifts of initial atomic and final molecular states arising from interaction with the background of ground-state atoms. Such a shift would be proportional to the atom density and depend upon the \(s\) -wave scattering lengths for atom-atom and atom-dimer collisions, \(a_{86}\)  and \(a_{\text{ad}}\)  respectively. This was observed in a Rb Bose-Einstein condensate (BEC) in [1]}. For a non-degenerate gas, this effect yields \(\chi _n=\hbar (\frac{a_{\text{ad}}}{\mu _{\text{ad}}}-4\frac{a_{86}}{\mu _{\text{aa}}})=\frac{\hbar }{m} (\frac{3 }{2}a_{\text{ad}}-8 a_{86})\) , where \(\mu _{\text{ad}}\)  and \(\mu _{\text{aa}}\)  are the reduced masses for molecule-atom and atom-atom collisions respectively. Note that the shift would vanish for \(a_{\text{ad}}=(16/3) a_{86}\) .
